Motion analysis and trials of the deep sea hybrid underwater glider Petrel-II

A hybrid underwater glider Petrel-II has been developed and field tested. It is equipped with an active buoyancy unit and a compact propeller unit. Its working modes have been expanded to buoyancy driven gliding and propeller driven level-flight, which can make the glider work in strong currents, as well as many other complicated ocean environments. Its maximal gliding speed reaches 1 knot and the propelling speed is up to 3 knots. In this paper, a 3D dynamic model of Petrel-II is derived using linear momentum and angular momentum equations. According to the dynamic model, the spiral motion in the underwater space is simulated for the gliding mode. Similarly the cycle motion on water surface and the depth-keeping motion underwater are simulated for the level-flight mode. These simulations are important to the performance analysis and parameter optimization for the Petrel-II underwater glider. The simulation results show a good agreement with field trials.


Introduction
Over the last ten years, conventional autonomous underwater vehicles (AUVs) and autonomous underwater gliders (AUGs) have played an increasingly significant role in oceanographic research due to their capabilities (Eriksen et al., 2001;Bachmayer et al., 2004). Owing to the difference in forward propulsion, AUGs can work continuously for several months at the horizontal speed of about 0.5 knot, while traditional propeller driven AUVs achieve an endurance ranging from hours to days at a speed of 2 knots (Claus et al., 2010(Claus et al., , 2012. Hence, AUGs may encounter a risk of mission failure when operated in strong-current area. Hybrid underwater gliders (HUGs) are therefore proposed for oceanic observations with high speed requirement.
A great deal of related scientific researches have been carried out. Bachmayer et al. (2004) proposed a prototype design of hybrid vehicle to improve cost efficiency. Wood et al. (2007) developed an autonomous self-mooring vehicle capable of autonomous mooring for oceanographic and meteorological data collection. Ambler (2010) and Reed et al. (2011), designed and developed a novel underwater vehicle for subsea equipment delivery. Wu et al. (2010) developed the prototype of HUG Petrel-I and conducted a series of field trials. Petrel-II investigated in this paper is developed to perform survey missions in oceans with strong currents on the surface . Petrel-II is equipped with one compact propeller unit, one active buoyancy unit, one attitude regulating unit, and fixed wings .
Till now, a variety of theories and approaches have been employed in dynamical modeling of underwater vehicles. Leonard and Graver (2001) and Graver (2005) derived a practical and detailed dynamic model of underwater glider with the first principles. Wang et al. (2007) built a dynamic model for a landing AUV using multibody theory. Motion capabilities were investigated and the layout of component was optimized based on dynamical analysis. Zhang et al. (2013) adopted a thorough approach analyzing the spiraling motion of AUGs. The analysis results show a good agreement with field trials. Wang et al. (2009) derived a nonlinear dynamic model for a thermal underwater glider by Gibbs and Appell equations to investigate the typical motions of the vehicle. Wang et al. (2011) treated HUG as a multibody system and developed a dynamic model based on mo-mentum theorem. Fan and Woolsey (2014) derived a nonlinear multi-body dynamic model for an AUG under an unsteady, nonuniform flow. In this paper, a 3D dynamic model of a low drag HUG Petrel-II is derived for vehicle motion analysis.

HUG Petrel-II
The HUG Petrel-II can glide using the buoyancy-driven system and maintain level flight using the propeller-driven system. During the glide mode, the vehicle dives and climbs in a zigzag trajectory through the water by varying the vehicle's buoyancy and using the control surfaces to translate buoyancy force into forward motion. During the levelflight operation, the vehicle can realize 2D and 3D motion.
Petrel-II is developed for long range, deep depth and high maneuverability ocean sampling missions. As shown in Fig. 1, Petrel-II consists of two wet sections and one sealed pressure hull, to which the wings and a tail antenna are attached. The pressure hull is composed of several sections, including the nose cap, the bow section, the middle section, and the stern section. The specifications of Petrel-II are summarized in Table 1  .

Kinematics of HUG
In order to describe the motions of HUG, three coordinate systems are established. As shown in Fig. 2, E-XYZ is the inertial coordinate system and the origin point E is fixed on the surface of the sea. The origin point of body-fixed frame (B-xyz) is located at the center buoyancy (CB) of the vehicle, and its coordinate axis are aligned with the axes of the vehicle and arranged by right-hand rule. The wind co-ordinate system O-abc has the same origin point with the body-fixed frame.
For the following analysis, we defined the position and orientation vector of the vehicle from inertial coordinate system and the linear and angular velocity vector of vehicle with respect to body frame as follows: where φ, θ and Ψ respectively represent the roll angle, pitch angle and yaw angle of the vehicle. According to the corresponding description in Graver (2005) and Wang et al. (2011), the kinematics for HUG can be written as: And the rotation matrix and can be described as: For the sake of writing conveniently, the first letters of sin, cos and tan function are used for abbreviation in this paper.

Forces and moments on HUG
HUG can be considered as a rigid body system when it conducts steady state motion in the water. Without consideration of the impact of water flow, the external forces and moments acting on the vehicle are shown below.
The gravitational, buoyancy forces and the righting moment of glider can be expressed in the body-fixed frame as: where r CG is the offset vector of CB with CG of the vehicle. It can be expressed in the body-fixed frame as: The additional buoyancy force and moment which are  caused by volume change of external bladder can be expressed in the body-fixed frame as: where r B is the position vector between CB of external bladder and CB of the vehicle. It can be expressed in the bodyfixed frame as: . The additional moment M r and M p can be written in the body-fixed frame as: where r p is the vector pointing from the initial position of CG of the eccentric mass package to its current position. It can be expressed in body-fixed frame as: . G p is the gravity force of the eccentric mass package.
According to Rong (2008), the forward thrust force F p and rotation-induced moment T p can be expressed in the body-fixed frame as: where K T and K Q respectively represent hydrodynamic coefficients of force and torque, ρ is the density of water, D represents the outer diameter of the propeller, and n is the rotational speed. According to Rong (2008) and Mahmoudian (2009), the hydrodynamic forces and moments of HUG are divided into viscous and inertial hydrodynamics components. A simple quasi-steady model for the hydrodynamic forces and moments take the following form: where ρV 2 /2 is the dynamic pressure, A represents the characteristic area of the vehicle, , , , , and respectively represent the coefficient of viscous hydrodynamic force and moment along the three coordinate axes of the body-fixed frame. p′, q′, and r′ are the dimensionless angular velocities, and p′=pl/v, , q′=ql/v and r′=rl/v. λ ** represents the added mass, added static moment and added moment of inertial.
Thus, the generalized external forces and moment acting on HUG in the body-fixed frame can be expressed as: 3.3 Dynamic modeling of HUG Let p and π represent the linear momentum and angular momentum of the vehicle in the inertial coordinate system, respectively. Let P and Π represent the linear momentum and angular momentum of the vehicle in the body-fixed frame, respectively. According to the vector translation relationship between the inertial coordinate system and the body-fixed frame, we have According to momentum theorem, we have where f i and t j represent the external force and pure external moment acted on the vehicle in inertial frame. l i is the distance vector between the original point of the inertial frame and external force f i . By differentiating Eq. (16) and Eq. (17) with respect to time and utilizing the expressions of kinematics, according to Eq. (18) and Eq. (19), the dynamic equations of HUG in body coordinates can be expressed as:

Parameter assignment
According to the derived dynamic equations, the characteristic parameters in the simulation of HUG motion are shown in Table 2 and Table 3.

Spiral motion
For the convenience of simulation, it is assumed that the vehicle moves in still water. The initial conditions of HUG are set as follows: The control parameters, B 0 , l p , δ and n are set as -2 N, 0.01 m, 0.9 rad, and 0 r/s, respectively. The simulation duration is 5000 s.
Based on the given control parameters, the spiral trajectory downward and changes in the parameters versus time are shown in Fig. 3. As illustrated in Fig. 3d, HUG achieves steady spiral downward movement. And the period of spiral motion is about 3900 s (Fig. 3b). It is shown in the simulation result that the turning radius is around 170 m (Fig. 3c) and the steady pitch angle is -30° (Fig. 3a). It is also indicated that the vehicle reaches a depth of 750 m within 3900 s ( Fig. 3b) with an average sinking velocity of 0.192 m/ s.

Surface navigation motion
The surface navigation motion of HUG includes surge and swerve. The initial conditions in the simulation are the same as the gliding motion simulation. The control parameters B 0 , l p , δ and n are set as 0 N, 0 m, 0 rad, and 15 r/s. The simulaiton lasts 40 s. In the swerve phase, the parameter δ is set as 1 rad. The simulation lasts 200 s.
The performances of the vehicle in the surface navigation motion are shown in Fig. 4. It can be observed from the simu-lation result that the maximum forward velocity is 1.15 m/s in surge stage (Fig. 4a), the period of cycle motion is about 150 s (Fig. 4c), and the turning radius is around 28 m (Fig.  4d).

Depth-keeping motion
The depth-keeping motion is the basic motion of HUG. The initial conditions in the simulation are the same as in the surface navigation motion. In the descent phase, the control parameters B 0 , l p , δ and n are set as 1 N, 0.01 m, 0 rad, and 5 r/s, respectively. The motion has been simulated for 200 s. Then, in the depth-keeping motion phase, the control parameters B 0 , l p , δ and n are set as 0 N, 0 m, 0 rad, and 14 r/s. The simulation duration is 300 s. In the ascent phase, the control parameters B 0 , l p , δ and n are set as -1 N, -0.01 m, 0 rad, 5 r/s, and the duration is 200 s. Fig. 5 indicates that HUG achieves steady gliding motion and depth-keeping motion with the prescribed control parameters. The steady pitch angle and the attack angle of the vehicle are about ±24.9° (Fig. 5c) and ±3.2° (Fig. 5b) respectively in the descending and ascending phases. It can also be observed that the vehicle reaches a depth of 40 m within 200 s (Fig. 5d) with an average sinking velocity of about 0.2 m/s. In the level flight phase, the steady forward velocity is about 1.06 m/s (Fig. 5a).

Field trials
Petrel-II had experienced two lake trials and two sea trials from December 2012 to April 2014 to testify the dynamic model and test vehicle in marine environment. More than 300 gliding cycles and 60 depth-keeping profiles were completed during the field trials. In April 2014, Petrel-II finished 219 continuous dives with the cruising range of 626 km. And in 2015, the cruising range was increased to more    LIU Fang et al. China Ocean Eng., 2017, Vol. 31, No. 1, P. 55-62 59 than 1100 km, which created a record of unmanned underwater vehicles in China at that time. Experiments on the gliding operation were conducted in the South China Sea (east latitude 111.0703°, north latitude 18.4042°) from July to September 2013, as shown in Fig. 6a. During the sea trials, more than 60 gliding cycles were finished. In the experiment, the control parameters were set the same as in motion simulation. The target depth was set to 160 m. Comparison between the results of the sea trial and the simulation results are demonstrated in Fig. 6. Fig. 6b shows the result in one gliding motion cycle. In the depth control algorithm test, Petrel-II adjusted the buoyancy to ascend when it reached the given "safe distance" to the target depth. Thus it took the vehicle about 750 s to arrive at the depth of 153 m when the target depth was 160 m. In addition, the vehicle's velocity changed with time due to the seawater density variation, buoyancy variation, and influence of currents. The average sink velocity was approximately 0.204 m/s. Fig. 6c shows that the equilibrium dive pitch angle is approximately -36° while the simulation value is -30°. Fig. 6d shows the temperature and conductivity of the vertical profile measured by CTD sensor installed on board. The experiment data fit well with the glide simulation results.
Experiments on the level-fight operation of Petrel-II were performed in Fuxian Lake, Yunnan, China. The experiments include surface navigation test and depth-keeping test. In the surface navigation test, the control parameters were the same as in motion simulation. The surface cruis-ing trajectory is shown in Fig. 7. Fig. 7a indicates that Petrel-II achieved a circular trajectory with the turning radius about 43 m. The deviation between the simulation and the experimental results may be due to currents and waves on the surface. In the depth-keeping operation, the control parameters were set the same as in the simulation and the target depth was set as 40 m. Fig. 7b shows the trajectory comparison between the simulation and experiment. It is shown that it took the vehicle about 200 s to arrive at the depth of 38 m with an average sinking velocity of about 0.19 m/s. In the depth-keeping phase, the depth gradually decreased due to a small positive pitch angle. Comparison between the simulation and the experimental results in the level-flight operation indicates that the dynamic model coincides approximately with the real model.

Conclusion
A multi-mission HUG, Petrel-II is developed as a lowdrag, light weight, large depth rating underwater vehicle for oceanic oceanography missions. The vehicle has a diving actuation and attitude adjustment mechanism as traditional AUGs. It is also capable of surface cruising and depth-keeping autonomously as self-propelled AUVs. In this paper, a dynamic model is established for Petrel-II utilizing linear momentum and angular momentum equations. Based on the model, the gliding motion patterns and the AUV motion patterns of HUG have been simulated. The simulation results agree well with the experimental results, verifying the feasibility and effectiveness of the dynamic model. Both the simulation and the experimental results show that the vehicle achieves stable status in the two operational modes. This work provides guidance for dynamical behavior prediction and system design improvements for HUG.